A wind turbine installation is usually formed of a support structure comprising an elongate tower, with a nacelle and a rotor attached to the upper end of the support structure. The generator and its associated electronics are usually located in the nacelle.
Fixed-base wind turbines that are fixed either to the land or the sea bed are well-established.
However, recently there has been a desire to develop floating wind turbines and various structures have been proposed. One example is a wind turbine installation where a conventional wind turbine structure is mounted on a buoyant base such as a platform or raft-like structure. Another proposal is a “spar buoy” type structure. Such a structure is formed of an elongate buoyant support structure with a rotor mounted on the top. The support structure could be a unitary structure or it could be an elongate sub-structure with a standard tower mounted thereon.
Floating wind turbine installations may be tethered to the sea bed via one or more mooring lines with anchors, or attached to the sea bed with one or more articulated (hinged) legs, for example, in order to hold them at their desired installation sites.
In conventional wind turbines, the pitch of the rotor blades is controlled on the basis of the rotor speed in order to regulate the power output. When operating in winds below a certain wind speed (which is referred to as the rated wind speed of a wind turbine), the blade pitch is kept approximately constant at an angle that provides maximum power output. In contrast, when operating above the rated wind speed, the blade pitch is adjusted in order to produce a constant power output and prevent excessively high power outputs that could damage the generator and/or its associated electronics. This constant power is referred to as the rated power of the wind turbine.
When operating below the rated wind speed, as the blade pitch is kept approximately constant, the thrust acting on the rotor increases with the wind speed (thrust being approximately proportional to the square of the wind speed).
In contrast, when operating above the rated wind speed the blade pitch is adjusted such that the thrust on the rotor decreases with increasing wind speed in order to produce a constant power output. As the wind speed increases, the blade pitch is increased, i.e. made more parallel to the wind direction, in order to reduce the thrust.
In practice, wind turbines operate in conditions both above and below their rated wind speed.
In order to produce maximum power output when operating below the rated wind speed, the blade pitch is set in order to produce an optimum tip speed ratio. The tip speed ratio, λ, is defined as the speed at which the outer tips of the rotor blades are moving divided by the wind speed and is given by:
                    λ        =                              ω            ⁢                                                  ⁢            R                    u                                    (        1        )            where ω is the angular frequency of the rotor (in radians per second), R is the radius of the rotor and u is the wind speed. An optimum tip speed ratio for maximum power output is around 8 to 10 and in most wind turbines this will in practice give a power coefficient Cp of around 0.45 (0.59 being the theoretical maximum), where the power P is defined as:
                    P        =                              1            2                    ⁢          ρ          ⁢                                          ⁢          A          ⁢                                          ⁢                                    C              p                        ⁡                          (                              λ                ,                β                            )                                ⁢                      u            3                                              (        2        )            where ρ is the air density, A is the area swept by the rotor blades and Cp is the power coefficient which is determined by λ and the blade pitch β.
As mentioned above, in order to produce a constant power output when operating above the rated wind speed, the blade pitch is adjusted in order to produce a constant rotor speed and thereby a constant power output. A problem associated with adjusting the blade pitch in this way is that it can cause negative damping, i.e. as the relative velocity between the turbine and the wind increases, the thrust force reduces. This can increase the amplitude of the wind turbine's oscillations or vibrations. Negative damping causes a reduction in the overall efficiency or power output of the wind turbine and, moreover, can create excessive motions that cause structural stresses which can damage or weaken the wind turbine structure and could cause instability in floating wind turbines. Negative damping can be a particular problem for high power (e.g. >2 MW) turbines.
Negative damping in fixed-base wind turbines arises because the turbine may vibrate forwards and backwards due to excitations of the tower's natural bending vibrations. As the wind turbine moves towards the wind, the relative wind speed acting on the wind turbine increases, which tends to increase the rotor torque or speed. Using the pitch control described above for constant power output, in response to an increase in the rotor torque or speed, the blade pitch angle is adjusted to reduce the torque acting on the rotor and, as a result, reduce the thrust and thereby maintain constant power. However, as the thrust is reduced, the damping force acting on the wind turbine's vibrations is also reduced and can become negative. In other words, the vibrations can be exacerbated and their amplitude increases. This then results in a further change in the relative wind speed and a further adjustment to the blade pitch, making the vibrations even larger. The opposite applies when the wind turbine is moving away from the wind, resulting in a further exacerbation of the vibrations.
The problem of negative damping is illustrated in FIG. 1, which shows the thrust force as a function of wind speed for a 2.3 MW turbine using the standard blade pitch control described above. The thrust force for wind speeds above 12 ms−1 decreases with increasing wind speed, and consequently negative damping may be introduced into the system in this wind speed range.
In fixed-base wind turbines, negative damping can be prevented or minimised by reducing the bandwidth of the blade pitch controller to lie below the natural frequency of the first order bending mode of the tower. In other words, the controller does not adjust the blade pitch for tower motions with frequencies above the natural frequency of the first order bending mode of the tower.
However, a floating wind turbine also has other modes of oscillation, besides the bending modes, which makes the problem of dealing with negative damping in floating wind turbines much more complex. Moreover, the prior art system discussed above does not deal with the most significant modes of oscillation in a floating wind turbine installation.
FIG. 2 shows a typical power spectrum for the oscillations of a typical floating wind turbine installation of the type having an elongate “spar buoy” type design. The scale on the vertical axis is proportional to the amplitude of the oscillations, which is proportional to the square root of the power of the oscillations. The scale on the horizontal axis is the frequency of the oscillations in Hz. The first line in the legend represents the oscillations present when standard pitch control (i.e. on the basis of the rotor speed) is used. The second line represents the oscillations present when vibration control for active damping of the support structure's bending mode vibrations is used (this is described below). The third line represents the oscillations present when pitch control according to the present invention is used (this will be discussed later).
The power spectrum has four main peaks. Only the fourth peak is also present in the power spectrum for a fixed-base wind turbine. The first three peaks are seen only in floating wind turbines.
The first peak occurs at frequencies of around 0.008 Hz and corresponds to the rigid body oscillations of the support structure[fG1] that are caused by the surge motion of the floating wind turbine coupled with the restoring effects of the mooring lines. In these oscillations the tower moves forwards and backwards horizontally but remains in an essentially vertical position. The size of this peak (i.e. the size of or energy in these oscillations) is not much affected by different approaches to pitch control. Generally the magnitude of these oscillations is not critical as the oscillations are very slow. Therefore, these oscillations do not suffer too much from negative damping. Furthermore, these oscillations do not result in large structural stresses on the tower. Consequently, these motions are accepted by designers and it is not necessary to try to prevent or minimise the negative damping of tower movements at these frequencies.
The second peak occurs at frequencies of about 0.03 to 0.04 Hz and corresponds to the rigid body pitch oscillations of the support structure (i.e. the “nodding” back and forth of the support structure). When blade pitch is controlled in order to produce a constant power output, the size of this peak (i.e. the size of or energy in these oscillations) increases dramatically due to the negative damping effect previously described, resulting in large structural stresses on the tower as well as oscillations in the power output. It is therefore desirable to prevent or minimise the negative damping of these oscillations.
The third, quite broad, peak occurs at frequencies of about 0.05 to 0.15 Hz. This corresponds to the rigid body wave-induced motion (surge coupled with pitch, but mostly pitch) of the floating wind turbine. The size of this peak can be minimised by modifying the geometry and weight distribution of the floating wind turbine but generally it is not desirable to do anything in relation to the damping of tower movements at these frequencies as the oscillations are not resonant and thus not very sensitive to the damping level. Attempts to damp this motion will normally result in large turbine forces without any significant impact on the motion response.
The fourth peak occurs at frequencies of about 0.3 to 0.5 Hz. As mentioned above, these oscillations are present in both floating and fixed-base wind turbines and correspond to the structural bending vibrations of the support structure.
As mentioned above, in order to prevent or minimise the negative damping of the structural bending vibrations, the bandwidth of the blade pitch controller may be reduced such that it does not adjust the blade pitch for motions that occur at these frequencies (i.e. 0.3 to 0.5 Hz).
However, in a floating wind turbine, whilst this approach can still be applied to address bending vibrations, if the bandwidth of the blade pitch controller were reduced even further such that the controller did not adjust the blade pitch for motions that occur at frequencies above those of the rigid body oscillations of the tower in pitch (i.e. 0.03 to 0.04 Hz), this would significantly reduce the bandwidth of the controller and would result in unacceptable performance with respect to key wind turbine properties such as power production, rotor speed and rotor thrust force. Therefore, in order to avoid or reduce negative damping in a floating wind turbine installation, it is not practicable to simply reduce the bandwidth of the controller in this way.
Most modern multi-megawatt wind turbines use a proportional integral (PI) controller to control the blade pitch to produce a constant rotor speed when operating above the rated wind speed of the turbine. The PI controller is a feedback controller which controls the blade pitch and thereby the rotor speed (i.e. the rotational frequency of the rotor) on the basis of a weighted sum of the error (the difference between the output rotor speed and the desired rotor speed) and the integral of that value. When the blade pitch control system is operating above rated power, the generator torque is typically controlled to produce either a constant torque or a constant power. The following description applies to constant power control. However, a similar approach applies to a generator with constant generator torque control at rated power.
For constant power control, the generator torque, Mgen, is given as:
                              M          gen                =                              P            0                    Ω                                    (        3        )            where P0 is the rated power for the turbine and Ω is the rotor speed in radians per second.
Equation (3) can be linearised around the rated rotor speed Ω0 to give:
                              M          gen                =                                            P              0                                      Ω              0                                -                                                    P                0                                            Ω                0                2                                      ⁢                          (                              Ω                -                                  Ω                  0                                            )                                                          (        4        )            
The aerodynamic torque on the wind turbine rotor, Maero, can be linearised around the actual blade pitch angle θ0 and the rated rotor speed Ω0 to give:
                              M          aero                =                                                            P                0                                            Ω                0                                      +                                          1                                  Ω                  0                                            ⁢                                                ∂                  P                                                  ∂                  θ                                                              ⁢                      ❘                          θ              0                                ⁢                      (                          θ              -                              θ                0                                      )                                              (        5        )            where it is assumed that variations in the rotor speed around the rated rotor speed Ω0 are negligible compared to variations in the blade pitch angle around the actual blade pitch angle θ0.
Then from Newton's second law, the equation of motion for the rotor is given as:
                              I          ⁢                                          ⁢                      Ω            .                          =                                            M              aero                        -                          M              gen                                =                                                    1                                  Ω                  0                                            ⁢                                                ∂                  P                                                  ∂                  θ                                                      ⁢                          ❘                              θ                0                                      ⁢                                          (                                  θ                  -                                      θ                    0                                                  )                            +                                                                    P                    0                                                        Ω                    0                    2                                                  ⁢                                  (                                      Ω                    -                                          Ω                      0                                                        )                                                                                        (        6        )            where I is the moment of inertia for the rotor and the generator, which is given by:I=Irotor+n2Igen  (7)where n is the gear ratio between the rotor and the generator, and θ is the blade pitch, which is given by:θ=θ0+Δθ  (8)where θ0 is the current blade pitch and Δθ is determined by the PI controller as:Δθ=θI+θP  (9)where:θI=∫KI(Ω−Ωref)dt=KIφ  (10)Ωref≡Ω0  (11)andθp=Kp(Ω−Ωref)=Kp{dot over (φ)}  (12)where Kp is the proportional gain and KI is the integral gain of the PI controller and {dot over (φ)} is the rotational frequency error (Ω−Ωref).
This leads to the following equation of motion for the rotor speed for the closed loop dynamic system:
                                                        I              ⁢                                                          ⁢                              φ                ¨                                      +                          D              ⁢                                                          ⁢                              φ                .                                      +                          K              ⁢                                                          ⁢              φ                                =          0                ⁢                                  ⁢        where                            (        13        )                                          D          =                                                    -                                  1                                      Ω                    0                                                              ⁢                                                ∂                  P                                                  ∂                  θ                                                      ⁢                          ❘                              θ                0                                      ⁢                          K              p                                      ⁢                                  ⁢        and                            (        14        )                                K        =                                            -                              1                                  Ω                  0                                                      ⁢                                          ∂                P                                            ∂                θ                                              ⁢                      ❘                          θ              0                                ⁢                                    K              I                        -                                          P                0                                            Ω                0                2                                                                        (        15        )            
Here, P is the power output and
            ∂      P              ∂      θ        ⁢      ❘          θ      0        ⁢      <    0.  The dynamic system in equation (13) can be stabilised by selecting appropriate values of the control parameters Kp and KI.
The natural frequency ω0, relative damping ζ, and damped resonance frequency ωd, of the closed loop system are then given by:
                              ω          0                =                                            K              I                                =                                                                                          -                                          1                                              Ω                        0                                                                              ⁢                                                            ∂                      P                                                              ∂                      θ                                                                      ⁢                                  ❘                                      θ                    0                                                  ⁢                                                      K                    I                                    -                                                            P                      0                                                              Ω                      0                      2                                                                                  I                                                          (        16        )                                          ζ          =                                    D                              2                ⁢                I                ⁢                                                                  ⁢                                  ω                  0                                                      =                                                                                -                                          1                                              Ω                        0                                                                              ⁢                                                            ∂                      P                                                              ∂                      θ                                                                      ⁢                                  ❘                                      θ                    0                                                  ⁢                                  K                  p                                                            2                ⁢                I                ⁢                                                                  ⁢                                  ω                  0                                                                    ⁢                                  ⁢        and                            (        17        )                                          ω          d                =                              ω            0                    ⁢                                    1              -                              ζ                2                                                                        (        18        )            respectively.
Generally, designers of control system for fixed foundation wind turbines try to keep the damped resonance frequency ωd below the first order bending frequency of the tower in order to avoid resonance. Typical values are ζ=0.7 and ωd=0.6 rad s−1.
The control systems of some fixed-base wind turbines also include a vibration controller to provide active positive damping of the first order bending mode vibrations of the support structure. An example of one such system is disclosed in GB 2117933. In these systems, positive damping is provided to cancel out, at least partially, any negative damping present, resulting in close to or approximately zero net damping of these vibrations. Alternatively, the positive damping may be large enough that, as well as cancelling out any negative damping, it also provides further positive damping, resulting in a net positive damping of these vibrations.
The vibration controller provides a correction to the blade pitch on the basis of measurements of the wind turbine structure's speed in order to damp the bending vibrations. The correction to the blade pitch is provided for wind turbine motions with frequencies that corresponds to those of the first order bending mode. The wind turbine's speed can be measured with a sensor such as an accelerometer with compensation for gravitational acceleration, for example. The speed measured may be the horizontal speed of the nacelle, for example, or its pitch speed (i.e. the absolute speed of the nacelle or a point on the tower due to motion in pitch).
An example of a control system with a vibration controller with active damping for a fixed-base wind turbine is shown in FIG. 3. The upper line in FIG. 3 is the active vibration controller part of the control system, which uses measurements of the tower velocity to prevent or minimise negative damping, as described above. The rest of the system is the standard controller which provides standard blade pitch control based on the rotor speed.
In FIG. 3, νnacelle, is the speed of the nacelle, hc(s) is the transfer function between the rotor speed error signal ωref and the blade pitch reference signal βref hp(s) is the transfer function between the blade pitch reference signal βref and the wind turbine rotor speed ωr, and Kd is the vibration controller gain.
In general, a transfer function gives the ratio between the Laplace transforms of the output and the input to a system component as a function of a variable s (where s is usually related to a spatial or temporal frequency, such as angular frequency).
The transfer function hc(s) can be provided by means of a PI controller in which case it can be expressed as follows:
                                          h            c                    ⁡                      (            s            )                          =                              K            p                    +                                    K              I                        s                                              (        19        )            where KI and KP are the integral and proportional gains of the PI controller, respectively, as described above, and have the following forms:
                                          K            I                    =                                    -                              (                                                                            ω                      0                      2                                        ⁢                    I                                    +                                                            P                      0                                                              Ω                      0                      2                                                                      )                                      ⁢                                          Ω                0                                                                                  ∂                    P                                                        ∂                    θ                                                  ⁢                                  ❘                                      θ                    0                                                                                      ⁢                                  ⁢        and                            (        20        )                                          K          P                =                  -                                    2              ⁢              I              ⁢                                                          ⁢                              ω                0                            ⁢              ζ              ⁢                                                          ⁢                              Ω                0                                                                                      ∂                  P                                                  ∂                  θ                                            ⁢                              ❘                                  θ                  0                                                                                        (        21        )            where the term
            ∂      P              ∂      θ        ⁢      |          θ      0      is negative and it varies with the actual blade pitch θ0.
The values of the parameters of the controller are determined by conventional tuning of the control system to the desired bandwidth.
The signal processing block in FIG. 3 will typically consist of some suitable filtering for removal of certain frequency components.
For the rest of the system, the loop transfer function h0(s) is defined as:h0(s)=hc(s)hp(s)  (22)and the expression for the rotational frequency of the rotor is given as:
                                          ω            r                    ⁡                      (            s            )                          =                                                                              h                  0                                ⁡                                  (                  s                  )                                                            1                +                                                      h                    0                                    ⁡                                      (                    s                    )                                                                        ⁢                          ω              ref                                +                                                                      h                  p                                ⁡                                  (                  s                  )                                                            1                +                                                      h                    0                                    ⁡                                      (                    s                    )                                                                        ⁢                          K              d                        ⁢                          v              nacelle                                                          (        23        )            
A measure of the control system's ability to follow the reference signal is given as:
                              M          ⁡                      (            s            )                          =                                            h              0                        ⁡                          (              s              )                                            1            +                                          h                0                            ⁡                              (                s                )                                                                        (        24        )            and the error between the desired reference signal and the measurement is given as:
                              N          ⁡                      (            s            )                          =                  1                      1            +                                          h                0                            ⁡                              (                s                )                                                                        (        25        )            
Considering equations (24) and (25) in the frequency domain (i.e. where s=jω) gives:|M(jω)|≈1 and ∠M(jω)≈=0when|h0(jω)|>>1  (26)|M(jω)|≈|h0(jω)| and ∠M(jω)≈∠h0(jω)when|h0(jω)|<<1  (27)
                                          N            ⁡                          (              jω              )                                ≈                                    1                                                h                  0                                ⁡                                  (                  jω                  )                                                      ⁢                                                  ⁢            and            ⁢                                                  ⁢            ∠            ⁢                                                  ⁢                          N              ⁡                              (                jω                )                                              ≈                                    -              ∠                        ⁢                                                  ⁢                                          h                0                            ⁡                              (                jω                )                                                    ⁢                                  ⁢                              when            ⁢                                                  ⁢                                                                          h                  0                                ⁡                                  (                  jω                  )                                                                            >>          1                                    (        28        )            N(jω)≈1 and ∠N(jω)≈0when|h0(jω)<<1  (29)and inserting equations (24) and (25) into equation (23) gives:ωr(s)=M(s)ωref+N(s)hp(s)Kdνnacelle  (30)
In order that the controller can satisfactorily follow the blade pitch reference signal, the parameters of the controller transfer function hc(s) must be tuned such that |h0(jω)|>>1 within the desired bandwidth of the control system. It therefore follows from equations (28) and (30) that N(s) will have a low absolute value within the bandwidth of the control system such that N(s) will suppress the response from hp(s)Kdνnacelle with frequencies within the bandwidth of the system. In other words, for frequencies within the bandwidth of the standard controller part of the blade pitch control system, active damping is suppressed and for vibrations with frequencies above or near the bandwidth of the standard controller part N(s) will have an absolute value of around 1 and these vibrations will be actively damped.
As noted above, in fixed-base wind turbines, the control parameters of the blade pitch controller are tuned such that the bandwidth of the standard part of the controller lies below the natural frequency of the first bending mode of the tower, in order to prevent or minimise negative damping of the structural bending oscillations. In addition, a vibration control part such as the one shown in FIG. 3 may be provided to provide active positive damping for vibrations with frequencies of the first bending mode since these vibrations have a frequency that is not suppressed by this part of the controller.
Also as mentioned above, floating wind turbines can also have structural bending vibrations with natural frequencies around 0.3 to 1 Hz. However, they also have rigid body oscillations with frequencies around 0.03 to 0.04 Hz.
If the control system in FIG. 3 were used in a floating wind turbine and the blade pitch controller parameters were tuned according to the frequency of the first structural bending mode of the tower, the active damping contribution N(s)hp(s)Kdνnacelle would provide positive damping of the high-frequency structural bending vibrations because the absolute value of N(s), according to equation (29), would be around 1 with very little phase lag for frequencies outside the bandwidth of the standard part of the control system. However, the contribution to the active damping of the low-frequency rigid body oscillations in pitch with frequencies around 0.03 to 0.04 Hz would be poor. These frequencies would be within the bandwidth of the standard controller part of the control system and the absolute value of N(s) would be low, according to equation (25), and therefore any active damping of these low frequency vibrations would be suppressed. Moreover, these frequencies would be within the bandwidth of the standard controller so the low-frequency rigid body oscillations of the support structure in pitch would suffer from negative damping.
At first sight it would appear possible to apply a similar approach to that used in fixed-base wind turbine installations in order to overcome negative damping of the rigid body oscillations in pitch in floating wind turbine installations. Thus, the controller parameters would be tuned according to the rigid body oscillations so that negative damping of both the structural bending vibrations and the rigid body oscillations of the structure would be prevented or minimised (because these motions would lie outside of the bandwidth of the standard part of the controller). Furthermore, the vibration controller part of the controller in FIG. 3 would then provide additional positive damping for both the rigid body oscillations and the structural bending vibrations since the absolute value of N(s), according to equation (29), would be around 1 with very little phase lag for these frequencies.
However, if the controller of FIG. 3 were tuned in this way, it would lead to a very slow blade pitch controller that would not react to changes in wind speed with periods of less than 30 seconds (i.e. with frequencies of more than 0.03 Hz). This would result in unacceptable performance with respect to key wind turbine parameters such as variations in power production, shaft torque, rotor speed, rotor thrust force, etc. This would in particular be the case for a floating wind turbine installation as the floating support structure would also move in response to the wave forces. Therefore, in order to achieve acceptable wind turbine performance in a floating wind turbine, it is not enough to simply tune the standard part of the controller in FIG. 3 to act only on lower frequencies. Rather, a new controller is required that is able to both suppress negative damping and provide active damping of the rigid body oscillations without also compromising the wind turbine's performance.
The inventors of the present invention have already developed a blade pitch controller for a floating wind turbine structure formed of a support structure comprising a tower supporting a rotor having a plurality of blades, the controller comprising standard blade pitch control means and active damping means. This controller is described in WO 2007/053031.